While current experimental demonstrations have been limited to small computational tasks, DNA strand displacement systems (DSD systems) hold promise for sophisticated information processing within chemical or biological environments. A DSD system encodes designed reactions that are facilitated by three-way or four-way toehold-mediated strand displacement. However, such systems are capable of spurious displacement events that lead to leak: incorrect signal production. We have identified sources of leak pathways in typical existing DSD schemes that rely on toehold sequestration and are susceptible to toe-less strand displacement (i.e. displacement reactions that occur despite the absence of a toehold). Based on this understanding, we propose a simple, domain-level motif for the design of leak-resistant DSD systems. This motif forms the basis of a number of DSD schemes that do not rely on toehold sequestration alone to prevent spurious displacements. Spurious displacements are still possible in our systems, but require multiple, low probability events to occur. Our schemes can implement combinatorial Boolean logic formulas and can be extended to implement arbitrary chemical reaction networks.